Using the continuity of $t$-conorm $\bot$ decomposable measure $m$ with respect to suitably chosen submeasure the completness of the semimetric space $(S,\Sigma,m)$ is proved. It is proved under some assumptions on a family $\mathcal S$ of sets in $(S,\Sigma,m)$, that either $\mathcal S=\Sigma$ or $\mathcal S$ is of the first Bair category in $(S,\Sigma,m)$.